Exploiting Mutual Fractional Synchronization to Improve Amplitude and Frequency Stability in Micromechanical Oscillators

In this paper we present our observations of the effect of mutual fractional synchronization of two oscillators created from two distinct resonance modes of a single micromechanical resonator on the noise of the oscillators. The modes have a 3: 1 fractional frequency ratio and by increasing the amplitude of the lower frequency mode the synchronization range will increase. We show by increasing the amplitude of the lower frequency mode, the white noise in frequency and amplitude of the higher mode will decrease. We show that when synchronized the frequency fluctuations of the higher frequency mode will reduce 4 times in comparison with the fluctuations of the same oscillator operating at the same amplitude when not synchronized. The same amount of reduction is also observed in the amplitude fluctuations of the higher frequency mode.